The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study what we call d-dimensional prime Catalan numbers, a sequence of numbers which count only a very specific subset of indecomposable balanced bracket expressions. We further introduce the notion of a trapezoidal diagram o...

The objective of this paper is to present multi-criteria group decision making in intuitionistic fuzzy environment based on grey relational analysis for weaver selection in Khadi institution. Weaver selection is a group decision making process involving qualitative and quantitative criteria. Intuitionistic trapezoidal fuzzy weighted arithmetic average operator and intuitionistic trapezoidal fuz...

Recently, we derived some new numerical quadrature formulas of trapezoidal rule type for the integrals I (1)[g] = ∫ b a g(x) x−t dx and I (2)[g] = ∫ b a g(x) (x−t)2 dx . These integrals are not defined in the regular sense; I (1)[g] is defined in the sense ofCauchy PrincipalValuewhile I (2)[g] is defined in the sense of Hadamard Finite Part. With h = (b − a)/n, n = 1, 2, . . ., and t = a+kh for...

In this paper, we investigate multiple attribute group decision making (MAGDM) problems where decision makers represent their evaluation of alternatives by trapezoidal fuzzy two-dimensional uncertain linguistic variable. To begin with, we introduce the definition, properties, expectation, operational laws of trapezoidal fuzzy two-dimensional linguistic information. Then, to improve the accuracy...

Throughout this report, polling systems play a central role. Polling systems are queueing systems consisting of multiple queues, attended by a single server. The server can only serve one queue at a time. Whenever the server moves from one queue to another, a stochastic, non-zero switch-over time is incurred. The server never idles; even when there are no customers waiting in the system, the se...

Abstract Numerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In multi-criteria decision-making (fuzzy MCDM) methods, information system control-theoretic models, qualitative are extracted from expert’s knowledge as linguistic variables modeled by linear/non-linear numbers...

In this study the performances of various non-circular microchannel heat sinks (normalized with circular shape) have been comparatively analyzed for CuO-water nanofluid and baseline pure water flow. Nusselt number and Poiseuille number for each microchannel and thermo-physical properties of CuO-water nanofluid (viz., thermal conductivity, viscosity, specific heat and density) have been designed...

Fuzzy Set Theory has been applied in many fields such as Operations Research, Control Theory, and Management Sciences etc. In particular, an application of this theory in Managerial Decision Making Problems has a remarkable significance. In this Paper, we consider a solution of Rectangular Fuzzy game with pay-off as imprecise numbers instead of crisp numbers viz., interval and LR-type Trapezoid...